The characteristic equation and minimal state space realization of
SISO systems in the max algebra

Reference:
B. De Schutter and
B. De Moor,
"The characteristic equation and minimal state space realization of
SISO systems in the max algebra," in 11th International Conference
on Analysis and Optimization of Systems (Sophia-Antipolis,
France, June 1994) (G. Cohen and J.P. Quadrat, eds.), vol. 199 of
Lecture Notes in Control and Information Sciences, Springer,
ISBN 3-540-19896-2, pp. 273-282, 1994.

Abstract:
In this paper we determine necessary and for some cases also
sufficient conditions for a polynomial to be the characteristic
polynomial of a matrix with elements in Rmax. Then we
indicate how to construct a matrix such that its characteristic
polynomial is equal to a given monic polynomial in Smax,
the extension of Rmax. We use these results to develop a
procedure to find a minimal state space realization of a single input
single output (SISO) discrete event system in the max algebra, given
its Markov parameters.